2051C06T1S

# 2051C06T1S - a(Q a" ’ fr Prof Tang MA2051 C06 Test 1 Section Name g Write Clearly Show Your Work I(25 Solve dy/dx(23inx y = sin x y(0)=8 by

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Unformatted text preview: ' a (Q, a " ’ fr; .- Prof. Tang MA2051 C06 Test 1 Section Name: g ----- Write Clearly, Show Your Work I. (25%) Solve: dy/dx + (23inx) y = sin x; y(0)=8 by using variation of parameters method. _ -9”- @ 126;). xolX' :82:ch .2m’)( 8': C 6 “Fl - @MW {9ch 6 W 7.; {g _L .. i H aim)? C: 62. :7 _ , -: Lon)! mm! my ‘ v : Lg; 4 103% l @IjngQ ‘1’“;[6 g. _ (j 16 ’2' +2., 2. (25%) Solve: du/dt + 2 u = e "2‘ + 3 where u = u(t). f . —}-. _ -119 r 1 A g 9? MLZQ ' “LEM/x @ (U094 7mm?“ do {Lit/“0i 3 L ,5. 52114342, 0)! L b (if cop/i 74w ' f A «PM: . 92 M 38 Ali-Z. 3. 1m dy/dx = 2x y2 . a) (5%) Is this equation linear? Why? No. 1'ka mg?’ m ems/m 2 7a- gs _ b) (10%) Can it be solved by separa ' - f variables? If no, Wh ‘9 . s, solve it. 9541?; F c) (10%) Let y(0)=2 and Ax=0.25. Use Euler's method to find y(0.5). 0 rs wa “jay” ~f \$5)ij X0: 0; yo -: L 9:1)‘93‘9: val +(K'919“)0X VEDWMI): gt {'HY'IVJOX 2— . : 2.+(1K0‘L>°clf=l 11+(2K0,Lfk"b owl" @ 22.9., . 4. A heat-1038 model is given by dT/dt = —2 (T—4). (—9 v; we. (19 :0 PS a-Mon/v foéuém‘ i'Iv/LZW“) a) (10%) Find the general solution; 4/15 * M 'Glzif ng-‘g (Wuf£;.(;¥; ‘ "7’6 - _ ("s a room, a b) (7%) Find the steady state solution if any; ‘39 - c) (8%) Is the steady state solution stable or unstable? Justify your answer (phaseline or limit methods are both fine). We Jaye/(ta . -— - {M d 5; yssv/ (‘5 maﬁa- hot?!” 146)," 4A,:- WWa-{l ...
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## This homework help was uploaded on 04/16/2008 for the course MA 2051 taught by Professor Tang during the Spring '08 term at WPI.

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2051C06T1S - a(Q a" ’ fr Prof Tang MA2051 C06 Test 1 Section Name g Write Clearly Show Your Work I(25 Solve dy/dx(23inx y = sin x y(0)=8 by

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